A lot of the filming sites are very spread out, so it's hard to suggest a place to stay. A lot depends on your budget, how many people are in your party, whether you have a car, etc.
There's a Hilton and a Best Western downtown, on the river, so a lot of filming sites are walkable from there. I'd say that's the one area that might feel the most like "Tree Hill." But, there's also an area near the intersection of Market and College Ave. that has a lot of hotels, with food, Target, etc. nearby.
I've never stayed downtown, but I have stayed at a few different places up near Market and College Ave. Personally, I don't like staying in hotels with exterior doors if I'm alone.
If you look through old threads in this section, I'm sure others have recommended hotels before. Also, check out Tripadvisor for reviews by people who have stayed in the hotels. Very helpful.
Sorry, I can't help with the newer sites. I used the list at the beginning of this thread, and the Star News link, when I first went looking for filming locations.